I was working on a new Org and was not able to open developer console for the new Org.
I came across the below fix for the issue
I just copy the https link (https://YOURORGANISATION.my.salesforce.com/_ui/common/apex/debug/ApexCSIPage) of the loading page and re-open a new web page, copy the link and the console this time open as usual in a new page.
You can save the url for future purpose if same issue reoccurs.